Energy and Luminosity reach

Our charge asks for evaluation of a baseline machine of 500 GeV with

energy upgrade to about 1 TeV. (the “about” came about due to the

specific proposals from Tesla and X-band of 800 and 1000 GeV, and

desire of parameters group not to prejudge the eventual choice).

The context of the energy and luminosity tradeoff is PHYSICS reach.

The LC is blessed with a set of questions, some of which have relatively

well specified energy reach (Higgs, top, precision Z and WW

production) and some that are indicative of rich payoff in the subTeV

region but are not specific as to energy and mass scale – Susy, models

with expanded gauge symmetries, extra dimensions…

Grannis

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In the Susy case, a successful program requires that certain states – the

partners of the leptons, gauge bosons and higgs – be seen and measured

reasonably accurately. In particular, getting enough information to

understand the kind of Susy that Nature chooses, and to extrapolate to the

Susy-breaking scale, requires that we see at least the low lying gauginos

(,

, and the sleptons.

Failure to get above the appropriate thresholds for these severely restricts

the physics, so the premium is upon having sufficient energy. Since we

don’t know now what the scale is, the ability to raise the energy when the

need arises is very important.

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Point 1 2 3 4 5 6 GeV GeV GeV GeV GeV GeV

336 336 90 160 244 92

494 489 142 228 355 233

650 642 192 294 464 304

1089 858 368 462 750 459

e e/920 922 422 1620 396 470

860 850 412 1594 314 264

Z h 186 207 160 203 184 203

Z H/A 1137 828 466 950 727 248

H+ H - 2092 1482 756 1724 1276 364

q q 1882 1896 630 1828 1352 1010

~

~ ~

~

~~

reaction

~ ~

336 336 90 160 244 92

494 489 142 228 355 233

650 642 192 294 464 304

1089 858 368 462 750 459

e e/920 922 422 1620 396 470

860 850 412 1594 314 264

Z h 186 207 160 203 184 203

Z H/A 1137 828 466 950 727 248

H+ H - 2092 1482 756 1724 1276 364

q q 1882 1896 630 1828 1352 1010

~

~ ~

~

~~

~ ~

RED: reactions accessible at 500 GeV

BLUE: reactions accessible at 1000 GeV

LHC Susy benchmark points.

Susy particles are pair produced – thresholds at sum of two masses

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For Strong Coupling models, little Higgs models, the new states (vector

quarks, techni-rho, new gauge bosons, etc.) are likely somewhat heavier

than 1 TeV, so evidence for these models will come from deviations in WW

scattering, modifications to gauge boson trilinear couplings, top quark form

factors etc. Here the advantage in higher energy is in magnifying these

‘loop effects’. The energy needed is thus not as clearly defined, but is

nevertheless real.

M= 1240 GeV M=2500 GeV

signifi

cance

Z Z

erro

r

Significance for technirho at LHC and LC at 500, 1000, 1500 GeV. (factor 6 gain in significance going from 500 → 1000 GeV.)

Error on anomalous trilinear gauge coupling at LHC, LC at 500, 1000, 1500 GeV. (error reduced by >2 going from 500 → 1000 GeV. Note: scale of in strong coupling models is 10-3

– 10-4.)4

A similar response to energy occurs for extra dimensions – the effects such

as mono-photons, modifications to cross sections etc. will vary rather

smoothly with energy. Production of mini black holes probably has a well

defined energy threshold.

Linear collider

Seeing Kaluza Klein states (Z’) requires energy sufficient to produce.

Raising energy magnifies the difference between # extra dimensions.

Gain going from 800 → 1000 GeV increases cross section by ~2.5 (D=8). Much more benefit from energy than luminosity.5

The important factor for precision is integrated luminosity, so peak luminosity

and the fraction of time the collider is producing collisions for physics are

equally important.

The gain in precision goes as √N (√ ∫Ldt )to a good approximation (providing

that systematic errors are data driven and setup time for special runs don’t

dominate, which we don’t think they will). Knowing results to higher precision

is good, but for many physics studies, a factor of 2 in ∫Ldt does not seem to

make a large difference.

Gaugino mass extrapolation

Here the main issue as I see it is in the

risk factor for actually attaining

reasonable ∫Ldt (Round table II)

e.g. for gaugino mass unification at

higher scale, the LHC errors already

dominate those at LC.

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Width of bands are errorsLHC

LC

SM value (decoupling limit)

approx. errors

Susy Higgs couplings to fermions, WW (ZZ) differ from SM as Susy parameters change. Precision BR measurements→ new physics

Susy couplings

Integrated luminosity does translate into crucial precision for Higgs BRs, and these in turn dictate the precision with which one can infer new non-SM physics such as MA in

MSSM. Expected precision with 500 fb-1

should give indirect MA up to about 600

GeV.

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So – more energy is good and more luminosity is good, but my reading is that getting higher energy is more important than higher luminosity. The LC will likely explore terrain where there are new particle thresholds. Sensitivity via loop effects to new phenemona at higher mass is improved through E increase faster than luminosity increase.

What does this mean?

I am not advocating that we aim at energies substantially above 1 TeV (another panel, another time). The prospect for superb physics at TeV scale is excellent.

I do regard the ability to go above the nominal top energy by 20-30%, even with lower luminosity, as an important advantage for physics.

Setting the stage for some future multi-TeV e+e- collider would be nice, but not crucial: our understanding of physics beyond the TeV scale is very unclear at this time and it may well be that the appropriate next step is a much higher energy hadron collider, 3 TeV CLIC, a very powerful proton-driver for neutrino physics, a 10 TeV lepton collider … We don’t have enough understanding to predict the right next step yet.

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